A satellite is carried by the Space Shuttle to a height of 10,000 miles from the center of the earth and released. The astronauts on the Space Shuttle need to know what the initial velocity of the satellite should be for it to attain the correct orbit.

What is known:

The radius of the earth is R_{E} = 3,960 miles.

The initial radius of the satellite from the center of the earth is r_{o} = 10,000 miles, which is 6,040 miles from the surface of the earth.

The initial velocity of the satellite will be parallel to the tangent to the earth's surface.

Question

What initial velocity should the satellite have if the orbit is to be
circular?

What is the minimum velocity required for the satellite to escape the
earth's gravitational pull?

If the initial velocity is 20,000 ft/s, what is the maximum radius of
the orbit?

Approach

Use polar coordinates and the equation that describes the free-flight
trajectory of an orbiting satellite.

Determine the relationship between the free-flight trajectory and
the eccentricity of a conic section.

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